Final answer:
The question involves geometry concepts such as angles in circles and congruent triangles. Accurate angle measures cannot be confirmed without a visual diagram, but the principles are based on a circle's full measure of 360 degrees and the congruency of geometric shapes.
Step-by-step explanation:
The provided information appears to be examining different geometric concepts related to angles, circles, and congruent triangles. Although the initial question seems to concern dividing a semicircle into three equal parts and identifying the measures of specific angles, the additional information discusses a variety of concepts such as measurements in degrees, the congruency of triangles under certain conditions, how angles correspond to arc lengths in circles, and basic properties of triangles. Without an accompanying figure, the precise matching of angle measures cannot be accurately provided; however, we can discuss the principles underlying these geometric considerations.
For instance, when dealing with circles, it's important to understand that a full circle contains 360 degrees, and therefore, dividing it into equal parts requires you to divide 360 by the number of divisions you want. In the case of angles in the sky or celestial navigation, knowing this allows for accurate measurements. Additionally, the congruency of triangles, such as those formed by celestial bodies and observational points, plays a crucial role in determining distances and angles in astronomical contexts.